Positive Externalities and Public Goods

This is Unit Twelve of Principles of Microeconomics: benefits that spill over, goods nobody can be kept from using, and resources everyone can take. Unit eleven was a cost that fell outside the price. This unit is the mirror image, a benefit that does, and then the extreme case: a good nobody can be kept from using, so nobody has to pay. The failures share one root, a missing property right. By the end you will be able to size the subsidy for a positive externality. To explain why competition discourages innovation and match a remedy to a spillover. To define a public good and classify any good in the two-by-two table. To set up the free-rider problem as a game. And to explain the tragedy of the commons and carry a levee and a fishery from failure to provision.

Three entries on the externality that runs the other way: a benefit that spills over, the two benefit curves, and the subsidy.

The externality that runs the other way.

MIC 1101 Positive Externalities

A positive externality is a benefit from a market exchange that lands on someone outside it: a vaccination protects the neighbors, and new knowledge spreads to firms that paid nothing. The buyer stops at their own benefit, so the market makes too few, and the failure mirrors unit eleven's.

The two benefit curves.

MIC 1102 Marginal Private Benefit and Marginal Social Benefit

Marginal private benefit is what the buyer gains from one more unit, and demand is drawn from it. Marginal social benefit adds the spillover and lies above demand, so the market quantity falls short of the optimum. Supply is marginal social cost here, and the optimum is where it meets social benefit.

The market with numbers.

MIC 1103 The Positive-Externality Market and the Subsidy

From demand, supply and an external benefit per unit, build the social benefit schedule by adding the spillover to what buyers will pay at each quantity. The market is where private demand meets supply; the optimum is where social benefit meets supply, at a larger quantity. The remedy is a subsidy to buyers equal to the spillover, which lifts demand onto social benefit, so that at the optimum sellers receive the higher price and buyers pay it less the subsidy. Private demand for flu shots meets supply at twenty dollars and eighty thousand. Each shot protects others by ten dollars, so society values ninety thousand shots at twenty-five, where supply offers ninety thousand: the optimum. A ten-dollar voucher lets buyers pay fifteen, at which they take ninety thousand, while clinics receive twenty-five, and ten thousand more shots are given. The subsidy equals the spillover per unit, not the quantity gap, and the voucher's treasury cost is efficient only because it was set at the external benefit.

Five entries on ideas and their remedies: why innovation spills over, the two returns, intellectual property, the other remedies, and matching remedy to case.

The externality in ideas.

MIC 1104 Why Competition Can Discourage Innovation

An innovator bears the research cost and risk. If rivals can copy quickly, the edge is small and brief, and studies put the inventor's share of the gain at a third to a half; the rest spills over. The spillover is the externality, and the shortfall it causes is underinvestment.

The two returns.

MIC 1105 Private Return and Social Return

A firm funds research while the private return covers the cost of borrowing. The social return, private plus spillover, is higher, so society would fund more projects. Education works the same way, hence the subsidy.

The first remedy.

MIC 1106 Intellectual Property

A patent gives an inventor the exclusive right to an invention for a period; copyright, for a work. The temporary monopoly profit is the reward competition would have removed. Patents are imperfect: inventors still capture a fraction, fast fields outrun them, and terms are arbitrary.

The other remedies.

MIC 1107 Funding, Tax Credits and Cooperative Research

Governments also fund research directly, through universities, labs and grants, with results made public; give tax credits for private research; and sponsor cooperation among firms and universities. Direct funding can be steered politically, and credits reward research that would have happened anyway.

Matching remedy to case.

MIC 1108 Which Remedy Fits

Given a spillover, ask three questions. Can the benefit be made excludable? If the output is a product, a patent or copyright lets the creator capture more. Is there a product at all? Basic research with none needs direct funding. Does the benefit land on identifiable buyers? If consumers create the spillover, a subsidy to buyers works; if firms create it, a tax credit or cooperative program does. Then state the trade-off. A drug copied in a month gets a patent, at the cost of a monopoly price; protein research with no product gets direct funding; flu shots get a voucher; an industry standard nobody will fund alone gets a cooperative program, watched for collusion. A patent trades one failure for another for a time, and no remedy makes the spillover disappear.

Three entries defining public goods: the two properties, what a public good is not, and the full classification.

The extreme case of spillover.

MIC 1109 Public Goods: Nonexcludable and Non-Rival

A public good has two properties. Nonexcludable: keeping a non-payer out is impossible or too costly. Non-rival: one person's use leaves as much for others, so the marginal cost of another user is zero. Test both: a slice of pizza fails both, a crowded road fails one.

What public goods are not.

MIC 1110 What a Public Good Is Not

Not every tax-funded good is a public good, and not every positive externality is one. Education has large spillovers, yet a private school can charge for it. The definition is about the good's properties, not who provides it.

The full classification.

MIC 1111 Classifying Goods by Excludability and Rivalry

Put any good in a two-by-two table: can a non-payer be kept out, and does one person's use leave less for others? Excludable and rival is a private good. Nonexcludable and non-rival is a public good. Nonexcludable but rival is a common resource, where open access leads to overuse. Excludable but non-rival is the fourth cell, which the course calls a club good: fenced, but free to share up to capacity. A slice of pizza is private, a lighthouse's beam public, fish in an open ocean a common resource, subscription satellite radio a club good, and an uncrowded toll road a club good that becomes rival at rush hour. Rivalry changes with congestion, so classify at the use level in question, and the table says how a good behaves in a market, not who ought to provide it.

Three entries on free riding and provision: why the nonexcludable cell fails, the game that shows it, and how public goods get paid for anyway.

Why the nonexcludable cell fails.

MIC 1112 The Free-Rider Problem

If nobody can be kept out, nobody has to pay. Each lets the others pay and rides free, and if all reason that way the good is never built, though all would gain. Free riding is the best reply to a good that arrives unpaid, not dishonesty.

The free-rider game.

MIC 1113 The Free-Rider Matrix

Set the free-rider problem up as unit nine's prisoner's dilemma. List each neighbor's choices, contribute or not, with payoffs as benefit minus contribution, and mark best replies. Not contributing is dominant for both, the Nash equilibrium is that nobody pays and the good is not built, and both would have done better contributing; a tax removes the choice and leaves the cell both preferred. A streetlight costs one hundred dollars and is worth eighty to each of two neighbors. Not paying beats paying whether the other pays, eighty against thirty, or does not, zero against minus twenty, so nobody pays and there is no light, though thirty each was available. A tax of fifty on each builds the light and leaves both with thirty. The tax is efficient only because the light was worth more than it cost, and the temptation to ride free grows with the group.

How public goods get paid for anyway.

MIC 1114 Provision of Public Goods

Governments provide public goods through taxes, which compel contribution. Markets provide some indirectly, as broadcast radio is paid by advertising, and others mix charges and social pressure. Taxes solve the free-rider problem, not the quantity question; how much defense to buy is left to politics.

Four entries to close: the tragedy of the commons, its remedies, and two capstones, a levee and a fishery.

The nonexcludable, rival cell.

MIC 1115 Common Resources and the Tragedy of the Commons

A common resource is nonexcludable and rival. Each user takes while it pays, ignoring the loss to others, so the resource is overused; Hardin named it the tragedy of the commons in nineteen sixty-eight. Economists read it as a property-rights problem: no owner, so nobody with reason to conserve.

The remedies.

MIC 1116 Remedies for the Commons

Remedies restrict access or create ownership: licenses, harvest limits, seasons, catch shares dividing a total allowable catch, or bans. Ostrom showed that users near a shared resource can manage it by their own rules. Both positions are attributed, and which prevails depends on whether users can see and sanction each other.

One public good from failure to provision.

MIC 1117 One Public Good: Why the Market Fails and Three Ways to Pay

Take a river levee for a town of a thousand households. It is nonexcludable, since once built it protects every house on the floodplain, and non-rival, since protecting one more house costs nothing. A builder who bills each household collects little, since each is protected whether it pays or not, and the levee is not built though it is worth more than it costs; the deadweight loss is its whole net benefit, forgone. Because every household consumes the same levee, the efficient height is where the sum of every household's gain from one more foot equals its marginal cost. Three ways to pay. Taxation removes the free-rider choice and the levee is built. Indirect provision ties the good to something excludable, though a levee has no such handle. Voluntary provision works where everyone is known and weakens as the group grows. The levee costs two hundred thousand dollars and is worth three hundred to each of a thousand households, three hundred thousand in all. Billed two hundred each, no household pays, since each gets the same protection for nothing, and a hundred thousand of net benefit is lost; a tax of two hundred each builds it, and every household nets one hundred. Three cautions. The tax solves the free-rider problem, not the quantity problem; politics can overbuild as easily as the market underbuilds. Nonexcludability, not government involvement, makes the levee a public good. And the deadweight loss is the net benefit forgone, not the whole value of the levee.

A resource that everyone can take.

MIC 1118 The Commons: One Fishery

A lake fishery is nonexcludable and rival. Under open access each owner enters while the average catch covers a boat, ignoring the catch taken from the others, so boats keep coming until the average only covers the cost and every boat earns nothing: the lake's rent dissipated in wasted boats. The efficient number is where the marginal catch equals the cost of a boat, which a single owner would choose. A license limit, a catch share divided into transferable rights, private ownership, or a community that watches itself: every remedy gives someone a reason to count the fish a boat takes from the others. Fish sell for a dollar and a boat costs fifty dollars a day. The marginal catch falls by ten from one hundred for the first boat. The efficient number is six boats, where the marginal catch of fifty equals the cost. The average catch at six boats is seventy-five, so more enter until, at eleven boats, the average equals the cost and profit is zero. A cap of six licenses, or a catch of four hundred fifty divided into shares, restores the rent. Three cautions. Open access means zero profit and a stock run down, not zero fish, and biological collapse can follow, which this example leaves out. Fixing the number of boats leaves each racing to catch first; catch shares end the race, which is why economists prefer them. And Hardin's word tragedy is about incentives, not character.

Look at what you can now do. You can define a positive externality, draw social benefit above demand, and set a subsidy equal to the spillover per unit so the market reaches the optimum. You can explain why an inventor keeps a third to a half of the gain, separate private from social return, and match a remedy to a spillover by asking three questions. You can define a public good by nonexcludability and non-rivalry and place any good in the two-by-two table. You can set the free-rider problem up as a prisoner's dilemma, show that a tax leaves the cell both preferred. And you can explain the tragedy of the commons as a missing owner, carry a levee from failure to provision, and run a fishery from open access to a cap that restores the rent. Unit thirteen turns to the market where most income is earned.